Results for Point Group S14



Symmetric powers of degenerate representation E1g
Vibrational overtones


Characters of symmetric powers
Power
To		 E C7 (C7)2 (C7)3 (C7)4 (C7)5 (C7)6 i (S14)9 (S14)11 (S14)13 S14 (S14)3 (S14)5
1 2 1.247 -0.445 -1.802 -1.802 -0.445 1.247 2 1.247 -0.445 -1.802 -1.802 -0.445 1.247
2 3 0.555 -0.802 2.247 2.247 -0.802 0.555 3 0.555 -0.802 2.247 2.247 -0.802 0.555
3 4 -0.555 0.802 -2.247 -2.247 0.802 -0.555 4 -0.555 0.802 -2.247 -2.247 0.802 -0.555
4 5 -1.247 0.445 1.802 1.802 0.445 -1.247 5 -1.247 0.445 1.802 1.802 0.445 -1.247
5 6 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 6 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
6 7 -0.000 -0.000 -0.000 0.000 0.000 0.000 7 -0.000 -0.000 -0.000 0.000 0.000 0.000
7 8 1.000 1.000 1.000 1.000 1.000 1.000 8 1.000 1.000 1.000 1.000 1.000 1.000
8 9 1.247 -0.445 -1.802 -1.802 -0.445 1.247 9 1.247 -0.445 -1.802 -1.802 -0.445 1.247
9 10 0.555 -0.802 2.247 2.247 -0.802 0.555 10 0.555 -0.802 2.247 2.247 -0.802 0.555
10 11 -0.555 0.802 -2.247 -2.247 0.802 -0.555 11 -0.555 0.802 -2.247 -2.247 0.802 -0.555
11 12 -1.247 0.445 1.802 1.802 0.445 -1.247 12 -1.247 0.445 1.802 1.802 0.445 -1.247
12 13 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 13 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
13 14 -0.000 -0.000 -0.000 0.000 0.000 0.000 14 -0.000 -0.000 -0.000 0.000 0.000 0.000
14 15 1.000 1.000 1.000 1.000 1.000 1.000 15 1.000 1.000 1.000 1.000 1.000 1.000
15 16 1.247 -0.445 -1.802 -1.802 -0.445 1.247 16 1.247 -0.445 -1.802 -1.802 -0.445 1.247
16 17 0.555 -0.802 2.247 2.247 -0.802 0.555 17 0.555 -0.802 2.247 2.247 -0.802 0.555
17 18 -0.555 0.802 -2.247 -2.247 0.802 -0.555 18 -0.555 0.802 -2.247 -2.247 0.802 -0.555
18 19 -1.247 0.445 1.802 1.802 0.445 -1.247 19 -1.247 0.445 1.802 1.802 0.445 -1.247
19 20 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 20 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
20 21 -0.000 -0.000 -0.000 0.000 0.000 0.000 21 -0.000 -0.000 -0.000 0.000 0.000 0.000


Decomposition to irreducible representations
Power
To		 Ag E1g* E2g* E3g* Au E1u* E2u* E3u*
1 0 1 0 0 0 0 0 0 E1g
2 1 0 1 0 0 0 0 0 Ag⊕E2g
3 0 1 0 1 0 0 0 0 E1g⊕E3g
4 1 0 1 1 0 0 0 0 Ag⊕E2g⊕E3g
5 0 1 1 1 0 0 0 0 E1g⊕E2g⊕E3g
6 1 1 1 1 0 0 0 0 Ag⊕E1g⊕E2g⊕E3g
7 2 1 1 1 0 0 0 0 2Ag⊕E1g⊕E2g⊕E3g
8 1 2 1 1 0 0 0 0 Ag⊕2E1g⊕E2g⊕E3g
9 2 1 2 1 0 0 0 0 2Ag⊕E1g⊕2E2g⊕E3g
10 1 2 1 2 0 0 0 0 Ag⊕2E1g⊕E2g⊕2E3g
11 2 1 2 2 0 0 0 0 2Ag⊕E1g⊕2E2g⊕2E3g
12 1 2 2 2 0 0 0 0 Ag⊕2E1g⊕2E2g⊕2E3g
13 2 2 2 2 0 0 0 0 2Ag⊕2E1g⊕2E2g⊕2E3g
14 3 2 2 2 0 0 0 0 3Ag⊕2E1g⊕2E2g⊕2E3g
15 2 3 2 2 0 0 0 0 2Ag⊕3E1g⊕2E2g⊕2E3g
16 3 2 3 2 0 0 0 0 3Ag⊕2E1g⊕3E2g⊕2E3g
17 2 3 2 3 0 0 0 0 2Ag⊕3E1g⊕2E2g⊕3E3g
18 3 2 3 3 0 0 0 0 3Ag⊕2E1g⊕3E2g⊕3E3g
19 2 3 3 3 0 0 0 0 2Ag⊕3E1g⊕3E2g⊕3E3g
20 3 3 3 3 0 0 0 0 3Ag⊕3E1g⊕3E2g⊕3E3g


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement